Question

At a youth group the 30 participants in a quiz are offered a drink and a snack. 16 have both a drink and a snack, 5 have a drink only and 3 have neither a drink nor a snack.

Answer 1

The number of people that had snacks only = n(D' n S) = 6

Explanation:

Let the set of people that have a drink be D

Let the set of people that have a snack be S

Universal set of all the people involved in the study = U

n(U) = 30

- 16 have both a drink and a snack

n(D n S) = 16

- 5 have a drink only

n(D n S') = 5

- 3 have neither a drink nor a snack.

n(D' n S') = 3

To now calculate the number of people that had snacks only, n(D' n S)

note that the universal set of all the people that participated in the study is given as

n(U) = n(D n S') + n(D' n S) + n(D n S) + n(D' n S')

30 = 5 + n(D' n S) + 16 + 3

n(D' n S) = 30 - 5 - 16 - 3 = 6

Hence, the number of people that had snacks only = n(D' n S) = 6

Hope this Helps!!!